Minimum Cost to Hire K Workers 🎯

Welcome to another engaging lesson on CodeYourCraft! Today, we're going to delve into the fascinating world of Data Structures and Algorithms, specifically focusing on the problem of finding the minimum cost to hire K workers. Let's get started!

Understanding the Problem 📝

Imagine you own a construction company and you need to hire K workers to complete a project. Each worker has a different hourly wage, and you want to minimize the total cost of hiring them. The challenge is to find the optimal combination of workers to minimize the total cost.

Algorithms and Data Structures Involved 💡

Greedy Algorithm: A simple, intuitive, and efficient algorithmic technique that makes the locally optimal choice at each stage with the hope of finding a global optimum.
Priority Queue (Min Heap): A data structure used to efficiently store and manage items that need to be frequently accessed with the highest or lowest priority.

Solution Approach 💡

Initialize an empty priority queue (min heap) to store workers.
Iterate through all the workers.
For each worker, if the priority queue is empty or the worker's hourly wage is less than the smallest wage in the queue, add the worker to the priority queue.
Once all workers have been processed, extract the K smallest wage workers from the priority queue.
Calculate the total cost by multiplying the number of each worker hired by their hourly wage and summing the results.

Code Example 📝

Here's a Python implementation of the solution:

python

from heapq import heapify, heappop, heappush

def find_min_cost(wages, k):
    # Initialize the priority queue (min heap)
    heapify(wages)

    # Keep track of the number of each worker hired
    worker_count = {w: 0 for w in wages}

    # Iterate through all workers
    for wage in wages:
        # If the priority queue is not empty and the worker's wage is greater than the smallest wage, skip the worker
        if wages and wages[0] > wage:
            continue

        # Add the worker to the priority queue
        heappush(wages, wage)

        # If the worker is one of the `K` to be hired, increment the counter
        if len(wages) <= k:
            worker_count[wage] += 1

    # Calculate the total cost
    total_cost = 0
    for wage, count in worker_count.items():
        total_cost += count * wage

    return total_cost

Quiz Time 💡

Stay tuned for more engaging lessons on CodeYourCraft! 📝